Question: Solve for $x$ and $y$ using substitution. ${-3x+4y = 11}$ ${y = -4x-2}$
Solution: Since $y$ has already been solved for, substitute $-4x-2$ for $y$ in the first equation. ${-3x + 4}{(-4x-2)}{= 11}$ Simplify and solve for $x$ $-3x-16x - 8 = 11$ $-19x-8 = 11$ $-19x-8{+8} = 11{+8}$ $-19x = 19$ $\dfrac{-19x}{{-19}} = \dfrac{19}{{-19}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -4x-2}\thinspace$ to find $y$ ${y = -4}{(-1)}{ - 2}$ $y = 4 - 2$ $y = 2$ You can also plug ${x = -1}$ into $\thinspace {-3x+4y = 11}\thinspace$ and get the same answer for $y$ : ${-3}{(-1)}{ + 4y = 11}$ ${y = 2}$